Question

Passar para a forma trigonométrica o numero complexo

Answer 1

Número complexo na forma trigonométrica

$\Large\boxed{\boxed{\boxed{\boxed{\sf{Z=\rho\left[cos(\theta)+i\,sen(\theta)\right]}}}}}$

Módulo de um número complexo z=a+bi

$\Large\boxed{\boxed{\boxed{\boxed{\sf{\rho=\sqrt{a^2+b^2}}}}}}$

Argumento de número

complexo

É o ângulo $\sf{\theta}$ tal que

$\sf{cos(\theta)=\dfrac{a}{\rho}~~~e~~~sen(\theta)=\dfrac{b}{\rho}}$

$\dotfill$

$\sf{z=\sqrt{3}+i}\\\sf{\rho=\sqrt{(\sqrt{3})^2+1^2}=\sqrt{3+1}=\sqrt{4}=2}\\\sf{cos(\theta)=\dfrac{\sqrt{3}}{2}}\\\sf{sen(\theta)=\dfrac{1}{2}}\\\sf{\theta=\dfrac{\pi}{6}}\\\sf{z=\rho\left[cos(\theta)+i\,sen(\theta)\right]}\\\Large\boxed{\boxed{\boxed{\boxed{\sf{z=2\cdot\left[cos\left(\dfrac{\pi}{6}\right)+i\,sen\left(\dfrac{\pi}{6}\right)\right]}}}}}$